Is this sentence gramatically correct? Is it acceptable to use the indirect object (us) here?
They proposed us a plan.
It definitely does not sound correct. The verb "propose" is almost always followed by the preposition "to" when connecting to an 'object' receiving the proposal. The object could be a person, a group of people (like a committee), etc. So, one correct way to write it would be
They proposed to us a plan.
Further, in this case, you should move the "a plan" part to just after the verb as well. So I would propose to you the following as the best usage in this scenario:
They proposed a plan to us.
The case where you do skip the "to" after propose while connecting it to people or a group of people would be when the person or the group itself is being proposed. For instance,
They proposed Robert for the post of CEO.
This link has some more examples of usage of the verb propose.